Question 9334: Solve each inequality. State the solution set using interval notation and graph the solition set.
4x^2 - 8x > or = 0
3x - x^2 > 0
Thanks in advance for your help.
Answer by mathmaven53(29)   (Show Source):
You can put this solution on YOUR website! 4x^2 - 8x >= 0
Factor left side
4x(x - 2) >=0
Then case I) 4x <=0 and x - 2 <= 0
so x <= 0 and x <= 2
So x <= 0
This is graphed on a number line by putting a solid dot at 0 and an arrow pointing to the left of point 0
case II) 4x >= 0 and x-2 >= 0
so x >= 0 and x >= 2
So x >= 2
The solution of 4x^2 - 8x >= 0 is x<= 0 or x>= 2
Interval notation of solution: (-infinity,0] or [2,infinity)
We graphed the first part of the solution
The second is graphed by putting a solid dot at point 2 on a number line and drawing an arrow to the right of this point
To solve 3x - x^2 > 0
factor left side
x(3 - x) > 0
Then case i) x < 0 and 3 - x < 0
x< 0 and 3 < x
This is false
so case ii) x > 0 and 3 - x > 0
x > 0 and 3 > x
0 < x < 3
Interval notation is (0,3)
To graph this solution, put open dots at points 0 and 3 on a number line
and draw a line segment between them.
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